1. Namas Chandra Introduction to Mechanical engineering Chapter 9-1 EML 3004C CHAPTER 9 Statics, Dynamics, and Mechanical Engineering

2. Namas Chandra Introduction to Mechanical engineering Chapter 9-2 EML 3004C Objectives Understand the concept of a Vector Write a vector in component form Understand the concepts of a couple and moment Construct a free-body diagram of a physical system Sections 9.1Introduction 9.2The Concept of a Vector 9.3Forces, Couples, and Moments 9.4Equilibrium and Free-body Diagrams 9.5Frictional Forces 9.6Motion of a Rigid Body

3. Namas Chandra Introduction to Mechanical engineering Chapter 9-3 EML 3004C 9.1Introduction  Statics deals with bodies (Solid, Liquid, Gases) that are in equilibrium with applied forces. At static equilibrium, a body is at rest or in constant motion (no acceleration).  Newton’s Law First: A body is at rest or in uniform motion (constant velocity) along a straight-line unless acted upon by some external (unbalanced) forces. Second: Every body accelerates in the direction of external forces. The acceleration is proportional to the magnitude of the force. Third: For every action, there is an equal and opposite reaction.  Statics is critical in the study of bodies under forces in the design. Free body diagram isolates forces/bodies and is a critical tool.

4. Namas Chandra Introduction to Mechanical engineering Chapter 9-4 EML 3004C 9.2Concept of a Vector  While scalar has only magnitude, e.g.: mass, temperature -vector has magnitude and direction, e.g. velocity, force, moment  The above is a geometric representation of the magnitude of the vector is unity, it is called a unit vector

5. Namas Chandra Introduction to Mechanical engineering Chapter 9-5 EML 3004C 9.2.1Component of Vector

6. Namas Chandra Introduction to Mechanical engineering Chapter 9-6 EML 3004C 9.2.2Component of Vector

7. Namas Chandra Introduction to Mechanical engineering Chapter 9-7 EML 3004C 9.2.3Direction Cosines of Vector

8. Namas Chandra Introduction to Mechanical engineering Chapter 9-8 EML 3004C 9.2.4Addition/Subtraction of Vectors  Since vectors have magnitude and directions only components can be added

9. Namas Chandra Introduction to Mechanical engineering Chapter 9-9 EML 3004C 9.3Forces, Couples, and Moments  Magnitude of a couple: M = Fd  Moment of a force M = Force x Lever arm  The direction of the moment is normal to the plane containing the force and the arm.

10. Namas Chandra Introduction to Mechanical engineering Chapter 9-10 EML 3004C 9.4Equilibrium and Free-Body Diagram  For static equilibrium, using Newton’s Second Law  Free body diagrams show all the forces and boundary conditions on a given body. Use the following steps Isolate the body from surroundings and draw a simple sketch Pick the right coordinate system (2D, 3D, Cartesian, Cylindrical) Add all extreme forces (right direction) and internal forces Label all known quantities (magnitude/direction )

11. Namas Chandra Introduction to Mechanical engineering Chapter 9-11 EML 3004C 9.5Frictional forces  A body on a surface (horizontal or sloped) is acted upon by weight acting vertically down and a reaction normal to the surface Using Coloumb’s Law for Static case  For bodies in motion,

12. Namas Chandra Introduction to Mechanical engineering Chapter 9-12 EML 3004C 9.5.2 Frictional Forces Given 15 Kg crate up 30 degree slope with

13. Namas Chandra Introduction to Mechanical engineering Chapter 9-13 EML 3004C 9.5.2 Frictional Forces..2 Given 15 Kg crate up 30 degree slope with

14. Namas Chandra Introduction to Mechanical engineering Chapter 9-14 EML 3004C 9.6Motion of Rigid Body

15. Namas Chandra Introduction to Mechanical engineering Chapter 9-15 EML 3004C 9.6.1 Crate Problem Revisited If the friction =0.3 compute the dynamics of motion?

16. Namas Chandra Introduction to Mechanical engineering Chapter 9-16 EML 3004C CHAPTER 9…concludes Statics, Dynamics, and Mechanical Engineering